## December 1

Saturday *from 4pm to 7pm and 9pm to midnight*, In room 102, Bethlen ter

*Putnam Mathematical Competition*

as has been announced several times, the Putnam exam will be offered
at Budapest for the registered BSM students.

Venue: BSM headquarters, Bethlen ter 2, room 102

Time: Saturday, December 1st, 4pm to 7pm ("morning session") and 9pm
to midnight ("afternoon session")

If you plan to participate, be there 10 minutes prior the beginning of each session.

You are not permitted to bring in any paper, books, slide rulers,
rulers, calculators, computers, etc., in the exam room. CELL PHONES
SHOULD BE TURNED OFF COMPLETELY. Participants should bring sharpened
pencils (or pens) and erasers.

## November 17

Sarturday * from 10:00 am to 15:00 pm*, In room 220 (next to BSM office), Bethlen ter

**BSM local mathematics competition **

The local math competition * comes with cash prizes * as well as serves as a selection for the team representing BSM at the
International Mathematics Competition for University Students 2013.
Anyone is very welcome to compete and the participation of good problem solvers is highly
encouraged!

## November 15

Thursday at *16:15*, In room 102, Bethlen ter

** BSM EUR Conference **

The Elective Undergraduate Research Groups will present their findings

## November 8

Thursday at *16:15*, In room 102, Bethlen ter

*Prof. Miklós Abért*, Rényi Institue: **Doubling a melon**

*Abstract:*
One can take a melon and a sharp knife, cut it to finitely many parts,
rearrange them and get two melons of the same size. That is, one can
exactly double the melon this way. This would effectively solve the
worlds hunger problem, but unfortunately, we have to use a very weird
shaped knife to make the cuts. Also, the thing wont work with
pancakes. Nor pasta.

Behind all this is a group theoretical notion called amenability. We
will define the notion, do the trick with the melon and show that
pasta and pancakes are no game. As a spice, we will use some
ultrafilters.

## October 25

Thursday at *17:00*, at Eotvos University, (Pazmany Peter setany
1/A - north building, "Északi tömb" - room 0-89; see remark below)

*Prof. László Lovász*, Eötvös University: **Why is it useful to walk randomly?**

*Abstract:* Doing a random walk on a graph is a tool with many applications: to
explore the structure of the graph; to generate a random node; to
find some hidden treasure; to prove properties of various geometric
structures. To make use of these applications, one has to study
basic properties of random walks, which is not always easy. The talk
will give a sampler of these studies and their applications.

*After the talk there will be chance to learn about the English language MSc program of the Institute of Mathematics of Eotvos University and tea given as well.*

*REMARK:*Another exceptional, out of the building colloquium lecture. The venue will be at the Eötvös University, Faculty of Sciences campus, north building (Északi tömb, 1/A on this map).

You find the Eotvos University campus by taking trams 4 or 6 southbound from Blaha Lujza, go with them across the Danube and leave the trams immediately on the Buda side. Walk along the Danube southbound until you reach the first of the two huge buildings of the Faculty of Sciences (North building)

A more detailed map of the immediate neighborhood .

Once you reach the north building ("Északi tömb") - which is the one closer to the bridge (and trams 4 and 6), the room is on the ground floor (see the plan of the building on this picture red cross showing the room and arrows the ways from the two entrances).

The time is 5:00pm, allowing all of you to reach the place.

Tea will be served after lecture, giving a chance to meet some of the faculty and math students of the Institute of Mathematics over there.

## October 18

Thursday at *16:15*, at BSM, in Room 102, Bethlen tér

*Prof. Aart Blokhuis*, Eindhoven University of Technology:
**Regular matchstick graphs in the plane**

*Abstract:* A matchstick graph is a planar unit distance graph,
so it can be realized by putting equal length, non overlapping
matchsticks in the plane. In the early eighties Heiko Harborth
asked for the smallest number of matches needed to produce regular
matchstick graphs of valency *k=1,2,3,4*. *k=1,2* and *3* are
easy party exercises, but *k=4* is hard, although we think we
know the answer. In 1982 I proved that a *5*-regular matchstick
graph does not exist, submitted the paper to Elemente der
Mathematik, but the paper was rejected for some reason.
I forgot about it until recently a paper in the American
Mathematically Monthly appeared, with essentially the same
proof (and acknowledging the existence of my 1982 manuscript).
In the talk I will present the (relatively elementary) proof.
See also http://mathworld.wolfram.com/MatchstickGraph.html.

## October 11

Thursday at *16:30*, at the Central European University (Zrinyi utca 14. 3. floor, room 310/A , Budapest, Hungary)

*Prof. András Stipsicz*, Central European University and Rényi Institute:
**Knots, colorings and polynomials**

*Abstract:* After reviewing basics of the theory of knots (i.e. knotted circles in
the 3-space), we show elementary methods for distinguishing knots from
each other. We define the Alexander polynomial of a knot, and describe
some recent advances and open problems in this classical chapter of mathematics.
We shall see many examples of such questions going from the simplest to quite complicated and examine what maximality (one of the most intriguing concepts of algebra) depends on.

*REMARK:*This will be the second lecture in the sequence introducing fine Hungarian higher education mathematics centers. CEU is an international graduate level university in the truest sense: Its students come from more than 80 countries; its faculty, from more than 30 countries--with the mix of nationalities increasing every year. The language of instruction and communication is English. It has it's own mathematics department and MSc and PhD math programs, which will also be shortly introduced. The venue of the lecture is the headquarters of the Department of Mathematics and it's Application at Zrinyi utca, downtown Budapest. You are assumed to find the location by yourself, with the following help: general directions general directions and map of the neighborhood.

## October 5

Friday at *16:45 (apprx.)*, at Bolyai Institute (Aradi vertanuk tere 1, Szeged, Hungary)

*Prof. Gergely RÖST: *, Bolyai Institute, University of Szeged:
**Introduction to delay differential equations with applications**

*Abstract: * As a first example, we consider the everyday showering
as a control problem, and introduce a class of delay
differential equations. Then we discuss the basic mathematical
questions for such equations: how to define a solution, what
is a suitable state space, what is the long term behavior
of solutions. In contrast to ordinary differential equations,
our equation generates an infinite dimensional dynamical system.
We look at some motivating examples from biology and economy,
and observe very complicated (even chaotic) behaviors of simple
looking nonlinear equations. Finally, some long standing
conjectures about the delayed logistic equation will be mentioned.

*REMARK:*This will be an exceptional, out of the town colloquium lecture at an exceptional time, Friday afternoon. This Friday the last classes (from 1pm) might be canceled (and made up later) and the group will leave from Nyugati railway station at 13:53 with TÖMÖRKÉNY intercity train. You will be met at the Szeged railway station at the arrival time, at quarter past 4 and be ushered to the site of the lecture. Mariann takes care of the train ticket (to Szeged) and the dormitory type accommodation, see her in case you intend to attend the lecture and visit Szeged.

## September 27

Thursday at*16:15*, in Room

*102*

*Feedback Session*

Having any problems in organizing your life in Budapest? We all come together on Thursday to help each other.

This is the perfect opportunity to discuss your first impression about the courses, instructors, and the BSM program. Your opinion can be valuable to us, as well as to others in making the big decision.

Also, the morning of this day is the deadline for registration. If you are uncertain what to keep and what to drop, the 'Feedback' will help to solve this clue. In any case, we finally have to form the classes, decide the fate of ones with low/high audience.

## September 20

Thursday*16:30*:

*"N is a number", a movie about Paul Erdős.*Please note that the movie will be shown in the Main Lecture Hall of the Renyi Institute, which you can find according to this map.

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